HIERARCHICAL MODEL OF SLOW CONSTRAINED DYNAMICS

We introduce a simple hierarchically constrained model of slow relaxat ion. The configurational energy has a simple form as there is no coupl ing among the spins defining the system; the associated stationary dis tribution is an equilibrium, Gibbsian one. However, due to the presenc e of hierarchical constraints in the dynamics the system is found to r elax to its equilibrium distribution in an extremely slow fashion when suddenly cooled from an initial temperature T-0 to a final one T-f. T he relaxation curve in that case can be fit by a stretched-exponential curve. On the other hand, the relaxation function is found to be expo nential when T-f>T-0, with characteristic times depending on both T-f and T-0, with characteristic times obeying an Arrhenius law. Numerical results as well as some analytical studies are presented. In particul ar, we introduce a simple equation that captures the essence of the sl ow relaxation.